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Pure Mathematics 2025
一类变分波动方程经典解的爆破
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Abstract:
针对一类一维非线性变分波动方程初值问题，应用特征线法和能量估计方法证明了即使初始能量任意小，经典解也会在有限时间内发生爆破。该模型源于受电场影响的向列相液晶体的研究。
We consider the initial value problem for a class of one-dimensional nonlinear variational wave equations. The method of characteristics and energy estimate is used to prove that the classical solutions will blow up in finite time even if the initial energy is arbitrarily small. This model is derived from the study of the nematic liquid crystals affected by electric fields.
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